Yes, the impact of adjacency bonus is much larger for Influence, Approval, and Food. They all work off a +1 scale, rather than the plus 0.05[aka 5%] like Manufacturing and Science.
BUG: Iridium Corporation don't receive Influence adjacency bonuses for any of their Influence buildings. Meaning they wouldn't even have the option to fight because their buildings are bugged.
Also some Influence bonuses apply to the entire amount. For ex.: Benevolent tree +100% Influence on capital applies to all Influence created there retroactively and in the future. If your capitals Influence was 100 when you selected the trait, it's now 200. So that's really powerful. And things that work in a similar manner, like planetary characteristics, will lead to you seeing two different numbers between the calculation within the Influence panel and the Total Influence.
Whether scale needs to be adjusted for adjacency bonuses for Influence, Approval, and Food is an area that should probably be revisited. Perhaps its okay for Food and Approval(though 0.5 seems more reasonable), but Influence could be like 0.1 and still be worthwhile.